Forward Interpolation Neural Network And Its Approximation Ability Based On Bernstein Polynomial And Ladder Shaped Path

A neural network is processing information by simulating the nerve and memory of human brain,which is an operation model that is usually interconnected by many neurons,it is a nonlinear dynamic system formed by a large number of neurons connected to each other.It is widely used in many resea.rch fields,especially in data mining,system identification and intelligent control.In fact,Neural networks process large amounts of data by imitating the unique structure of the human brain,and they can be used to solve the problem of multiple inputs and multiple outputs that are difficult for traditional computers.Therefore,it is of important theoretical significance to construct a multi-input forward neural network with approximation performance.Chapter one:Introduction,introduces the background and research status of this topics.Chapter two:Preparatory knowledge,introduce Bernstein polynomials and its approxima-tion theorem,and introduce three-layer forward neural network with single input and single out-put(SISO).three-layer forward neural network with two input and single output and its corre-sponding topology diagram.Chapter three:A three-layer forward interpolation neural network is designed by using the difference value and the Sigmodial transfer function property of unary Bernstein polynomial at the adjacent equidistant section points,and the method of selecting the connection weight and the threshold of the network is given.In addition,the SISO three-layer interpolation neural network is proved to be approximate to continuous function according to unary Bernstein polynomial ap-proximation continuous function theorem.and then an analytic expression of input and output is obtained.Chapter four:Firstly.equidistant subdivision is carried out for the two-dimensional input space,and the connection weight and threshold are selected based on the difference value and arithmetic mean value of the points of the adjacent subdivision,and then the three-layer forward interpolation neural network model is constructed according to the ladder shaped path of two-dimensional equidistant subdivision.Secondly,it has proven that the two-input three-layer forward neural network has approximation to continuous functions by using the properties of the Sigmodial transfer function,and the construction method of two-dimensional interpolation network is extended to n-dimensional case.Finally.the approximation performance of the two-input three-layer forward neural network is compared corresponding to the different ladder shaped paths.